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college algebra--please

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I am not understanding this question and I have read the chapter many times. Please help.

given the function of f(x)=4x-8

a. find the the rate of change between the stated values for x:5 to 7

b. find the equation of a secant line containing the given points (5,f(5)), and (7,f(7))

Like I said I have no clue. Can you please show me how you got the answer please?

  • college algebra--please -

    rate of change is (change in y)/(change in x)

    f(5) = 12
    f(7) = 20

    y changes from 12 to 20 as x changes from 5 to 7:

    rate of change is thus (20-12)/(7-5) = 8/2 = 4

    Note that the rate of change is the same as the slope of the line f(x)=4x-8

    The secant line is thus the line from (5,12) to (7,20). Or, it is the line from (5,12) with a slope of 4. Either way, you get

    (y-12) = 4(x-5)
    y = 4x -8

    This is not surprising, since the secant joining any two points on a line is just a section of the same line.

    It strikes me as odd that such a problem is posed. Could it be that the function is

    f(x) = 4^x-8. Probably not, as the values of f(x) would be quite large.

    Oh well, if the function is wrong, just use the method above to find the secant.

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